Therefore the solution to this problem is the test statistic for the test is -0.487
What is test statistics ?
In statistical hypothesis testing, a test statistic is a statistic that is employed. A hypothesis test is often defined in terms of a test statistic, which is a numerical summary of a data set that can be used to execute the test and reduces the data to one value.
Here,
According to a report on the evening news show, burglaries occurred in 23 out of 197 residences without pets and 10 out of 129 homes with pets.
Let p1 represent the percentage of dog-owning homes who experienced burglaries.
p2 is the population proportion of burglarized homes without canine companions.
Since both population proportions are equal, the null hypothesis (H) is that p1=p2.
A Different Hypothesis, K:p1≠p2 indicates that there is an imbalance between the two population proportions.
The test results that would be utilized in this z-test for proportions with two samples;
T.S. = [tex]\frac{(p1^{'} -p2^{'} )-(p1-p2)}{\sqrt{\frac{p1^{'}1-p1^{'}()}{n1} +\frac{p2^{'}(1-p2^{'})}{n2} } }[/tex]~ N(0,1)
where, p1= sample proportion of households with pet dogs who were burglarized =10/105 = 0.095
p2= sample proportion of households without pet dogs who were burglarized = 24/212 = 0.11
n1= sample of households with pet dogs = 105
n2 = sample of households without pet dogs = 212
So, the test statistics = [tex]\frac{(0.0095 -0.11 )-(0)}{\sqrt{\frac{0.095(1-0.095)}{105} +\frac{0.11(1-0.11)}{212} } }[/tex]
= -0.487
Therefore ,the test statistic for the test is -0.487
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